Progressive metal is indeed drawing influence from progressive rock, with the simplest example being the complexity. But, as in many other genres, progressive metal has gone way too far to be considered progressive rock anymore. (and you don't need to cite sources from encyclopedias or communities; just think about what you're listening to.) I would prefer progressive rock although I wouldn't deny that I like progressive metal as well.

Accepting and incorporating external influences more than the other one in context.

Aha. That's also a bit too tricky for genre designation. I've seen that a lot of people have these principle genres and anything that comes that is hard to be designated as such would either require them to come up with a new tag that would describe them as a fusion of those principle genres, or just write down the correlated principle genres down, just like what happens with Post-metal when some people instead use progressive metal, sludge metal and doom metal to describe it.

IMO having the ability to categorize is really essential because you can't simply put Asphyx in the same category as Marduk, but I find it to be overkill if it turns into a obsession. (e.g Asphyx being categorized as post-death/doom) Distinction exists among music bands and projects and the borderlines are obvious.

Aha. That's also a bit too tricky for genre designation. I've seen that a lot of people have these principle genres and anything that comes that is hard to be designated as such would either require them to come up with a new tag that would describe them as a fusion of those principle genres, or just write down the correlated principle genres down, just like what happens with Post-metal when some people instead use progressive metal, sludge metal and doom metal to describe it.

Indeed. An example would be the progarchives site where people use such terms like Eclectic prog, Neoprog, progfolk etc. It might seem totally unnecessary but for those who are extremely into prog, that might actually help categorize it more for the sheer number of bands they will have if they only use the tag as "Prog rock". I think it actually does help. But at the same time people should just listen to prog and enjoy it and not obsessed with categorizing into genres and labelling everything. Even if they are all called just "prog rock" that still wouldn't make them any less enjoyable.